using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;

using E = System.Linq.Enumerable;

internal partial class Solver {
    public void Run() {
        var n = ni();
        var q = ni();
        var a = ni(n);

        var tree = new LazySegmentTreeMulAndAddMonoidOperator().CreateLazySegmentTree();
        tree.Build(n, i => {
            var x = a[i];
            int mod = 0;
            if (x % 2 != 0) {
                mod = 1;
                x--;
            }
            return new Data { Div2Sum = x / 2, Mod2Sum = mod };
        });

        for (int _ = 0; _ < q; _++) {
            var t = ni();
            if (t == 1) {
                var l = ni() - 1;
                var r = ni() - 1;
                tree.LazyUpdate(l, r + 1, new MulAndAddOperatorMonoid {
                    Mod = true,
                });
            } else if (t == 2) {
                var l = ni() - 1;
                var r = ni() - 1;
                var x = ni();
                tree.LazyUpdate(l, r + 1, new MulAndAddOperatorMonoid {
                    Add1 = x,
                });
            } else {
                var l = ni() - 1;
                var r = ni() - 1;
                var x = tree.Query(l, r + 1);
                cout.WriteLine(2L * x.Div2Sum + x.Mod2Sum);
            }
        }
    }
}


public interface ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> {
    TMonoid Merge(TMonoid left, TMonoid right);
    TMonoid Apply(TMonoid monoid, int dataNum, TOperatorMonoid operation);
    TOperatorMonoid MergeOperator(TOperatorMonoid current, TOperatorMonoid append);

    TMonoid Identity { get; }
    TOperatorMonoid OperatorIdentity { get; }
}

public static class LazySegmentTreeExtension {
    public static LazySegmentTree<TMonoid, TOperatorMonoid> CreateLazySegmentTree<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator) {
        return new LazySegmentTree<TMonoid, TOperatorMonoid>(lazySegmentTreeMonoidOperator);
    }

    public static bool Check<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator, TMonoid m, TOperatorMonoid o1, TOperatorMonoid o2) {
        var r1 = lazySegmentTreeMonoidOperator.Apply(lazySegmentTreeMonoidOperator.Apply(m, 1, o1), 1, o2);
        var r2 = lazySegmentTreeMonoidOperator.Apply(m, 1, lazySegmentTreeMonoidOperator.MergeOperator(o1, o2));
        return r1.Equals(r2);
    }
}

public sealed class LazySegmentTree<TMonoid, TOperatorMonoid> {
    private readonly ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> monoidOperator;

    private int Count;
    private TMonoid[] node;
    private TOperatorMonoid[] operators;
    private int[] height;
    private int[] dataNum;
    private readonly TMonoid identity;
    private readonly TOperatorMonoid operatorIdentity;

    public LazySegmentTree(ILazySegmentTreeMonoidOperator<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator) {
        monoidOperator = lazySegmentTreeMonoidOperator;
        identity = lazySegmentTreeMonoidOperator.Identity;
        operatorIdentity = lazySegmentTreeMonoidOperator.OperatorIdentity;
    }

    public void Build(IList<TMonoid> array) {
        Build(array.Count, i => array[i]);
    }

    public void Build(int n, Func<int, TMonoid> create) {
        Count = n;

        node = new TMonoid[2 * Count];
        operators = new TOperatorMonoid[2 * Count];
        dataNum = new int[2 * Count];
        height = new int[2 * Count];
        for (int i = 0; i < node.Length; i++) {
            node[i] = identity;
            operators[i] = operatorIdentity;
        }

        for (int i = 0; i < n; i++) {
            node[i + Count] = create(i);
            dataNum[i + Count] = 1;
        }

        for (int i = 2; i < height.Length; i++) {
            height[i] = height[i >> 1] + 1;
        }

        for (int i = Count - 1; i > 0; i--) {
            node[i] = monoidOperator.Merge(node[i << 1], node[i << 1 | 1]);
            dataNum[i] = dataNum[i << 1] + dataNum[i << 1 | 1];
        }
    }

    private void Propagate(int k) {
        int childL = k << 1, childR = childL | 1;
        operators[childL] = monoidOperator.MergeOperator(operators[childL], operators[k]);
        operators[childR] = monoidOperator.MergeOperator(operators[childR], operators[k]);
        node[k] = Apply(k);
        operators[k] = operatorIdentity;
    }

    public TMonoid Query(int begin, int end) {
        TMonoid lv = identity, rv = identity;
        begin += Count;
        end += Count;
        TopDownOperators(begin);
        TopDownOperators(end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { lv = monoidOperator.Merge(lv, Apply(l++)); }
            if ((r & 1) == 0) { rv = monoidOperator.Merge(Apply(r--), rv); }
        }
        return monoidOperator.Merge(lv, rv);
    }

    public void LazyUpdate(int begin, int end, TOperatorMonoid @operator) {
        begin += Count;
        end += Count;
        TopDownOperators(begin);
        TopDownOperators(end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { operators[l] = monoidOperator.MergeOperator(operators[l], @operator); l++; }
            if ((r & 1) == 0) { operators[r] = monoidOperator.MergeOperator(operators[r], @operator); r--; }
        }
        BottomUpMonoids(begin);
        BottomUpMonoids(end - 1);
    }

    private void TopDownOperators(int k) {
        for (int i = height[k]; i > 0; i--) {
            Propagate(k >> i);
        }
    }

    private TMonoid Apply(int k) {
        return monoidOperator.Apply(node[k], dataNum[k], operators[k]);
    }

    private void BottomUpMonoids(int k) {
        while ((k >>= 1) > 0) {
            node[k] = monoidOperator.Merge(Apply(k << 1), Apply(k << 1 | 1));
        }
    }

    public TMonoid this[int index] {
        get {
            index += Count;
            TopDownOperators(index);
            return Apply(index);
        }
        set {
            index += Count;
            TopDownOperators(index);
            node[index] = value;
            operators[index] = operatorIdentity;
            BottomUpMonoids(index);
        }
    }
}


// example

public struct Data {
    public long Div2Sum;
    public long Mod2Sum;
}

public struct MulAndAddOperatorMonoid {
    public long Add1;
    public bool Mod;
    public long Add2;
}

/// <summary>
/// query       : a1 + a2 + ... + an
/// range-update: a <- a * Mul + Add
/// </summary>
public class LazySegmentTreeMulAndAddMonoidOperator : ILazySegmentTreeMonoidOperator<Data, MulAndAddOperatorMonoid> {

    public Data Identity { get { return new Data(); } }
    public MulAndAddOperatorMonoid OperatorIdentity { get { return new MulAndAddOperatorMonoid(); } }


    public Data Merge(Data left, Data right) {
        return new Data {
            Div2Sum = left.Div2Sum + right.Div2Sum,
            Mod2Sum = left.Mod2Sum + right.Mod2Sum,
        };
    }

    public Data Apply(Data monoid, int dataNum, MulAndAddOperatorMonoid operation) {
        //var sum = (1L * monoid.Sum + 1L * operation.Add1 * dataNum);
        if (operation.Mod) {
            if (operation.Add1 % 2 != 0) {
                operation.Add1--;
                var carry = monoid.Mod2Sum;
                monoid.Mod2Sum = dataNum - carry;
                monoid.Div2Sum += carry;
            }

            monoid.Div2Sum = 0; // mod 2

            if (operation.Add2 % 2 != 0) {
                operation.Add2--;
                var carry = monoid.Mod2Sum;
                monoid.Mod2Sum = dataNum - carry;
                monoid.Div2Sum += carry;
            }
            monoid.Div2Sum += operation.Add2 / 2 * dataNum;

        } else {
            if (operation.Add1 % 2 != 0) {
                operation.Add1--;
                var carry = monoid.Mod2Sum;
                monoid.Mod2Sum = dataNum - carry;
                monoid.Div2Sum += carry;
            }
            monoid.Div2Sum += operation.Add1 / 2 * dataNum;

            if (operation.Add2 != 0) throw new Exception();
        }
        return monoid;
    }

    public MulAndAddOperatorMonoid MergeOperator(MulAndAddOperatorMonoid current, MulAndAddOperatorMonoid append) {
        if (!current.Mod && !append.Mod) {
            return new MulAndAddOperatorMonoid { Add1 = current.Add1 + append.Add1 };
        } else if (current.Mod && !append.Mod) {
            // a1 mod a2 b1
            return new MulAndAddOperatorMonoid {
                Add1 = current.Add1,
                Mod = true,
                Add2 = current.Add2 + append.Add1,
            };
        } else if (!current.Mod && append.Mod) {
            // a1 b1 mod b2
            return new MulAndAddOperatorMonoid {
                Add1 = current.Add1 + append.Add1,
                Mod = true,
                Add2 = append.Add2,
            };
        } else {
            // a1 mod a2 b1 mod b2
            var a1Mod2 = current.Add1 % 2 == 0 ? 0 : 1;

            return new MulAndAddOperatorMonoid {
                Add1 = a1Mod2 + current.Add2 + append.Add1,
                Mod = true,
                Add2 = append.Add2,
            };
        }
    }
}

// PREWRITEN CODE BEGINS FROM HERE
internal partial class Solver : Scanner {
    public static void Main(string[] args) {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

internal static class LinqPadExtension {
    [Conditional("DEBUG")]
    public static void Dump<T>(this T obj) {
#if DEBUG
        LINQPad.Extensions.Dump(obj);
#endif
    }
}

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        int i = 0;
        bool negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) throw new FormatException();
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new InvalidOperationException();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) break;
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}